Question

A diver jumps off a diving board. The diver's height above the water, in meters, is represented by the function , where t is the number of seconds since the diver jumped. How high above the water is the diver after 2 seconds? How high above the water is the diver after 3 seconds?

Answer 1

To determine the highest point above the board, the time the diver's feet are in the air, and the velocity upon water impact, we apply kinematic equations considering the initial velocity, the starting height, and gravity as acceleration.

Step-by-step explanation:

Given that a diver jumps from a board with an initial velocity of 4.00 m/s and a starting height of 1.80 m above the water, we can solve different aspects of the motion using the equations of kinematics under the influence of gravity, assuming acceleration due to gravity is -9.81 m/s2.

• To find the highest point above the board, we use the equation v2 = u2 + 2as, where v is the final velocity (0 at the highest point), u is the initial velocity, a is the acceleration due to gravity, and s is the displacement (the height gained).
• The time the feet are in the air can be found using the equation s = ut + 0.5at2, where s is the total vertical displacement when the diver hits the water (1.80 m downwards), u is the initial velocity, a is the acceleration, and t is the time.
• To calculate the velocity when the feet hit the water, we use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time taken to hit the water.

Performing these calculations requires solving quadratic equations and using proper physical units.